Units Digit

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money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pmFollowed by: 79 members; Location: New Jersey; Thanked: 109 times; GMAT Score:640

by money9111 » Sat Feb 06, 2010 12:51 pm

What is the units digit of (2^5)(3^3)(4^2). How do you figure this out without multiplying all of the powers?

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Source: Beat The GMAT — Problem Solving | Sat Feb 06, 2010 12:51 pm

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sat Feb 06, 2010 12:51 pm

the ans is 4

just check out for the unit digit of all the terms..
for every number after a certain power unit's digit repeat ..
like for 2^5 unit digit repeats after 4, unit digit of 2^5 =2
for 3 unit digit repeat after 4, unit digit of 3^3 =7
for 4 unit digit repeat after 2, unit digit of 4^2 = 6

now multiply 2* 7*6 = 84... so unit digit will be 4..

here u have to multiply because u have given powers as 5,3,2
If u have some big powers then it will take same time as this question.. so main funda is to stick up with the unit digit like a bug and follow the theory that unit digit always repeat after certain multiplication. and u can easily solve the problem.

Last edited by shashank.ism on Sat Feb 06, 2010 1:01 pm, edited 2 times in total.

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Osirus@VeritasPrep: GMAT Instructor; Posts: 1578; Joined: Thu May 28, 2009 8:02 amFollowed by: 34 members; Thanked: 128 times; GMAT Score:760

by Osirus@VeritasPrep » Sat Feb 06, 2010 12:54 pm

Set it up like this

2
----------------

1(power) 2nd power 3rd power 4th power

2 4 8 6

After the fourth power it repeats, so the units digit of 2^5 would be 2. You would set up a similar table for each number and then multiple each unit digit together.

The answer would be 2 * 7 * 6= 84 Units digit equals 4

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akahuja143: Master | Next Rank: 500 Posts; Posts: 182; Joined: Mon Apr 20, 2009 7:09 pmFollowed by: 1 member; Thanked: 1 times

by akahuja143 » Sat Feb 06, 2010 12:56 pm

Ans is 4..

Before I type up the my explaination, osirus0830 explained it nicely.

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money9111: Legendary Member; Posts: 2109; Joined: Sun Apr 19, 2009 10:25 pmFollowed by: 79 members; Location: New Jersey; Thanked: 109 times; GMAT Score:640

by money9111 » Sat Feb 06, 2010 1:10 pm

I understood shashank.ism's answer the best...

thank you!

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